Without detailed calculation of all information, it looks like you take on the gift donor's basis of $1 plus her work of 180,000 and your work if you did not deduct taxes and utilities previously, of 190,000. If you rent out the place or you lived in the place, the calculation will be different. Be aware. Then, you should have closing cost to get the house ready for sale. Therefore, if you sell the place for 240,000, you should have sold it for a loss of (1+180,000+190,000+ closing cost) - $240,000. You probably sold it at a long-term capital loss. Please find a professional CPA to make sure all calculations are done correctly.
If you sold it for a long-term capital gain and you are on social security disability, it does not matter to your eligibility to the disability income, because disability counts only earned income, i.e., wages and/or self-employment income. If you are on regular social security disability and/or retirement income, the taxable portion of your social security could increase if your capital gain increases.
Below link is on what counts for your basis to that real estate property.
You want to document what improvement your mother did. Taxpayer's oral testimony can be counted as evidence. You document now is better than later. There are also many ways to document. For example, the county assessment office could have increase the house value in the past because of the improvement done on the house. Below IRM section 188.8.131.52 states what can be considered as evidence during IRS examination. Therefore, it is a good reference for us to use on how to document her improvement on the house.
Please feel free to follow up.
Fiona Chen, MPA, Ph.D., CPA, ABV, CFF, CITP